Consider the following linear operators defined on \(\mathcal {O}(\mathbb {D}_{R}),\)  (see [1]} for more details),
\(\;Q:\psi \longmapsto Q\psi (z):&=& \psi (qz),\\\; P:\psi \longmapsto P\psi (z):&=&\psi (pz),\\\;\partial _{p,q}:\psi \longmapsto \partial _{p,q}\psi (z):&=&\frac{\psi (pz)-\psi (qz)}{z(p-q)},\) 
